Is it permissible to name an endowed water well with a supplication such as, "O Allah, have mercy on me, and forgive me, and pardon me," instead of naming it with a personal name, with the intention that it be an ongoing charity and that Allah may answer the supplication through it?

It is better not to write the name on the charity, as it is closer to sincerity, and because concealing charity is better than showing it, unless there is a legitimate purpose for showing it, such as encouraging people, in which case showing it is better. There is no harm in naming the well with the aforementioned name.